# A change machine changes dollar bills into quarters and nickels. lf you receive 12 coins after inserting a dollar bill, how many nickels did you receive?

Dec 4, 2016

$10$

#### Explanation:

If we write $n$ for the number of nickels (5c) and $q$ for the number of quarters (25c), then we have two simultaneous equations:

$100 = 25 q + 5 n$

$12 = q + n$

Dividing both sides of the first equation by $5$ we get:

$20 = 5 q + n$

Multiplying both sides of the second equation by $5$ we get:

$60 = 5 q + 5 n$

Subtracting the previous equation, we find:

$40 = 4 n$

Dividing both sides by $4$ and transposing, we find:

$n = 10$

So there were $10$ nickels, making $50$c and $2$ quarters, making the other $50$c.